Generalized Euclidean operator radius inequalities of a pair of bounded linear operators

Let B(H) represent the C^*-algebra, which consists of all bounded linear operators on H, and let $N ( .) $ be a norm on B(H). We define a norm w(N,e) (. , . ) on B²(H) by w(N,e)(B,C)=|λ₁|²+λ₂|²≤1 θ N( (eiθ(λ₁B+λ₂C))), for every B,C(H) and λ₁,λ₂. We investigate basic properties of this norm and prove some bounds involving it. In particular, when $N( .)$ is the Hilbert-Schmidt norm, we prove some Hilbert-Schmidt Euclidean operator radius inequalities for a pair of bounded linear operators.